Not OP but most of my savings have been on time, rather than money. It did save some money.

* When installing a portable AC, I noticed that the included window kit didn't extend far enough. Similarly, another window was small, and the window kit would have to be sawed off. They retail for approximately $50 for a piece of plastic. Printer cost me $150. Plastic costs were under $10. Thats close to 2/3 of the printer price right there.

* One of the air conditioners came with a broken caster(bought online). Store didn't help. I could return the entire unit, but I would have to endure a heat wave without one. So I just printed an adaptor to use with some other furniture casters I had laying around. Designing was quick, so in a couple of hours I had my issue fixed.

* Printed a Raspberry Pi case. A few more bucks.

* My mom is starting a business and she needed some tools (really, they are guide pieces, ridiculously simple but you need relatively precise measurements). Some people would either purchase them (double digit dollars for one) or create crappy versions using cardboard. I designed and printed those for her and saved almost a hundred bucks, for something that almost looks like it came from a store. Plus I can further customize to her needs.

* Printed a stand for my soldering iron. It's a DS-80p so it is tiny, the 'normal' stands are incredibly bulky. Printed a version I found on Thingiverse. While at it, why not print a nice case for it too, right?

* Wanted to use the macbook upright, in clamshell mode. I could buy some stand, costing $20 and up. I didn't need anything fancy, so I just printed one. For about one tenth of the price of the cheapest option I could find. I got it in the same day even.

* Due to COVID, printed a bunch of face shields.

* Holders for a variety of things.

Then there are some pure convenience:

* Bike reflector holder piece broke. I wanted to go out to ride. Printing a replacement took less time than going to the store and back. Debatable if money was saved but not having to leave the house (or wait for a package) was certainly nice. Doubly so after COVID.

* I wanted some desk grommets of a specific size (and length). Checked Amazon, they were either overpriced or came in larger quantities than I need and I would end up with an assortment of surplus pieces. Whatever, Thingiverse, fired up the printer, off I go. I even customized for the exact thickness of the desk.

* Decided it would be cool if my Steam controller rested upright on a desk. Absent-mindedly queued a job remotely to the printer. Estimated costs around $1.

I could go on and on for a day. But it's not a matter of seeing what I or others have printed and going "Oh I need that". It's about what it brings to the table.

The bottom line is this. Assuming you have:

* Some time to learn the basics of a CAD tool (any tool).
You most likely don't need anything too complex. Most useful objects have simple shapes, you just need the ability to adapt them to your situation.
You can get pretty far with downloading models online - sometimes I get surprised of what niche objects you can find. But often you can't find some specific thing you are looking for (the AC examples above) and you need to design.

* Some time (and patience) to learn the basics of 3D printing and to do some troubleshooting when things go wrong. There's all sorts of communities that can help but you still need the basics.

Then what you end up with is the ability to just conjure up stuff when you need a problem fixed. Anything. Maybe you need to hang something, maybe something moves and it shouldn't. Or maybe it doesn't but should (I've used skate rollers with 3d printed pieces, works great). Maybe some tiny plastic piece broke and the manufacturer is charging an arm and a leg to replace. You can just find it (if you are lucky or if it is a common thing) or you can design it yourself.

This also allows you to come up with a bunch of DIY projects as this thread shows.

If it is made out of plastic and fits in the build plate, odds are you can make it, unless it requires a more exotic plastic.